Calculus (3rd Edition)

by
Rogawski, Jon; Adams, Colin

Published by
W. H. Freeman

ISBN 10:
1464125260

ISBN 13:
978-1-46412-526-3

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises: 13

Answer

$f'(x) = \dfrac{7}{2\sqrt{7x-3}}$

Work Step by Step

In order to derivate this function you have to apply the chain rule
Let's make an «u» substitution to make it easier
$u = 7x-3$
$f(u) = \sqrt{u}$
Derivate the function:
$f'(u) = \dfrac{u'}{2\sqrt{u}}$
Now let's find u'
$u' = 7$
Then undo the substitution, simplify and get the answer:
$f'(x) = \dfrac{7}{2\sqrt{7x-3}}$